Final note of caution:
Experiments like these have the inherent chance of rising your fame with your local sysadmin if you're doing them on a filesystem that's part of his backup plan, or critical for the well-being of the system.
Depending on his choice of tool for backup, he might end up needing more tape media than he ever considered possible to back up that one 0-byte file which gets expanded to terabytes of zeroes.

Other files which cannot be copied with neither cat nor cp would include device-special files, etc.
It depends on your implementation of copying tool if it is able to duplicate the device node, or if it would merrily copy its contents instead.

So cp makes a file just like the original, while cat creates a new file with the same content.
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TheoYouJan 30 '12 at 15:29

Both tools operate on content, but cp (at least "modern" implementations) is aware of some specialities nowadays, like holes (old implementations of cat will run into that trap). There also are filesystems which are unaware of the concept of sparse files, for example HFS+ (MacOS) or FAT (MSDOS, USB-Sticks, etc), causing them to be blown up to their full size. So there are constellations where cp or cat won't make a difference in practice.
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Tatjana HeuserJan 30 '12 at 15:47

According to Keith's comment, cp preserves some permissions, and cat creates the new file as umask indicates. So $2's permission is not preserved that $4/vmlinuz is pretty clean, while if some strange permission is set on $3, $4/System.map will keep that.

There is technically no real difference unless you use the cp command with the -p switch to preserve file ownership/group. Otherwise, it's the same thing functionally. Marc's answer is much more clearly verbose though and accurate.

Both have equivalent functionality in those two cases, but cp is purely a file operation. "Take this file and make a copy of it over there".

cat, on the other hand, is intended to dump the contents of a file out to the console. "Take this file and display it on the screen" and then have a ninja attack the screen and redirect the output elsewhere.

cp would generally be more efficient, as there's no redirection going only, merely a direct copying of bytes from location A to location B.

cat won't really output to console -> intercept output -> redirect to new file, output file for cat can be stdout or a normal file, it'll just output to the file, as long as input is not the same as output.
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TheoJan 29 '12 at 3:14

2

cat has nothing to do with the console. Both cat and cp read from the input file and write to the output file. With cat, the output file is opened by the shell, whereas with cp, the output file is opened by cp; this makes no difference in performance. cp may be faster, but for a completely different reason: some implementations of cp try to guess the right chunk size for performance depending on the source and target devices; an implementation of cat wouldn't bother.
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GillesJan 29 '12 at 23:48